Given -
A cone and a cylinder have equal radii = r,
and equal altitudes = h
The slant height of the cone = l
To Find -
The ratio of the lateral area of the cone to the lateral area of the cylinder =?
Step-by-Step Explanation -
The lateral surface area of the cylinder = 2πrh
The lateral surface area of the cone = πrl
So,
The ratio of the lateral area of the cone to the lateral area of the cylinder =
[tex]\begin{gathered} \frac{The\text{ }lateral\text{ }surface\text{ }area\text{ }of\text{ }the\text{ }cone}{The\text{ }lateral\text{ }surface\text{ }area\text{ }of\text{ }the\text{ }cylinder}\text{ = }\frac{\pi rl}{2\pi rh} \\ \\ =\text{ }\frac{l}{2h} \end{gathered}[/tex]Final Answer -
The ratio of the lateral area of the cone to the lateral area of the cylinder =
A. l:2h
